A takes twice as much time as B and thrice as much as C to completen a piece of work. They together complete the work in 1 day. In what time, will A alone complete the work.

9 days

5 days

6 days

4 days

Solution

Let time taken by C to complete
the work = x days
∴ Time taken by A to complete
the work = 3x days
and time taken by B to complete
the work = \(\frac{3x}{2}\) days
According to the question
\(\frac{1}{3x}+\frac{1}{\frac{3x}{2}}+\frac{1}{x}=1\)